The history of chess isn't especially clear - there's few country within the world that does not claim to possess invented it, including China, Egypt, Greece, Uzbekistan and (most unbelievably) Ireland.
Given the evidence, however, it seems presumably than the sport of chess has its origins in 6th century India, and was then refined in Persia, from where it travelled to Europe and far afterward to America.
The word 'chess' itself is believed to be a mangled pronunciation of the Persian word 'shah', which suggests king (and remains used today, as in 'Shah of Iran'). 'Checkmate', during this theory, comes from 'shah mat', which is Persian for 'the king is finished'.
Chess is notable within the development of games because it doesn't use dice, meaning that there's no element of luck involved - it's a game of pure skill and strategy. One Indian legend has the sport being created by a mentor who was asked by a king to make a game that might enhance his mental abilities and don't have anything to try to to with luck.
While India is keen to say chess, however, it's hotly disputed. Most Chinese people believe that China invented chess, and also believe that the sport is way inferior to travel, which is both older and usually considered harder. The Chinese means that Go has existed since a minimum of 2,000BC, and is played without dice, making it a really likely inspiration for chess.
Iran (Persia), on the opposite hand, claims that chess springs from its invention of backgammon, and cite writings and poems that appear to place its date further back than the Indian version. there's no doubting that the version of chess that came to Europe we play today came mainly from Persia, but it's difficult to understand exactly where Persia got its inspiration from.